A certain amount is distributed among $A, B$ and $C$. $A$ gets $\frac{3}{16}$ and $B$ gets $\frac{1}{4}$ of the whole amount. If $C$ gets ₹ 81, then $B$ gets
(a)₹ 30
(b)₹ 32
(c)₹ 36
(d)₹ 40
Answer
Answer (as printed): C
Explanation
Let the whole amount be ₹ $x$. Then, A's share $=₹\left(\frac{3}{16} x\right) ;$ B's share $=₹\left(\frac{x}{4}\right)$; and C's share $=₹\left[x-\left(\frac{3 x}{16}+\frac{x}{4}\right)\right]=₹\left(\frac{9 x}{16}\right)$. $$\therefore \quad \frac{9 x}{16}=81 \Leftrightarrow x=\left(\frac{81 \times 16}{9}\right)=144 .$$ Hence, B's share $=₹\left(\frac{144}{4}\right)=₹ 36$.
Explanation as extracted from the printed page; notation may be imperfect.